Composite materials are increasingly finding use in structures, such as aircraft components,
and thus, an accurate method of predicting response is required. Even laminated structures that
are considered thin can be significantly affected by transverse shear effects, and as a result,
transverse shear should not be neglected. The free vibration response of generally-laminated,
thick, skew, trapezoidal plates is investigated as there appears to be a lack of information in
this area. In the method developed, Chebychev polynomials are used as displacement
functions in the Rayleigh-Ritz method. Various edge supports are considered, and appropriate
linear and rotational springs are introduced to approximately satisfy the essential boundary
conditions associated with simply-supported and clamped edges. First-order shear theory is
used to account for transverse shear effects, and rotary inertia is also included.in the model.
Convergence of the solution resulting from changes in spring values and number of terms in the
series is investigated. The accuracy of the method is demonstrated by comparing the present
method to available results for plates of various quadrilateral shape, material systems, and
boundary conditions. Thick laminated plates of both symmetric and unsymmetric construction
and of various planforms and boundary conditions are then presented. Cantilever, thick, skew,
and trapezoidal plates are then extensively studied, and variations in natural frequencies due
to geometric parameter changes, such as taper ratio, sweep angle, and value of the parameter q, are discussed. The parameter, q, is a root length multiplier which determines the length of the
quarter-chord line, thus representing a measure of the span. Mode shapes for a number of plates
of various planform and support conditions are included.
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